hSrSSKrSSKJr SSKJr /SQr\"S5\RS55r \"S5\RS 55r \"S5\RS 55r g) zDProvides functions for computing the efficiency of nodes and graphs.N)NetworkXNoPath)not_implemented_for) efficiencylocal_efficiencyglobal_efficiencydirectedcbS[R"XU5- nU$![a SnU$f=f)aReturns the efficiency of a pair of nodes in a graph. The *efficiency* of a pair of nodes is the multiplicative inverse of the shortest path distance between the nodes [1]_. Returns 0 if no path between nodes. Parameters ---------- G : :class:`networkx.Graph` An undirected graph for which to compute the average local efficiency. u, v : node Nodes in the graph ``G``. Returns ------- float Multiplicative inverse of the shortest path distance between the nodes. Examples -------- >>> G = nx.Graph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)]) >>> nx.efficiency(G, 2, 3) # this gives efficiency for node 2 and 3 0.5 Notes ----- Edge weights are ignored when computing the shortest path distances. See also -------- local_efficiency global_efficiency References ---------- .. [1] Latora, Vito, and Massimo Marchiori. "Efficient behavior of small-world networks." *Physical Review Letters* 87.19 (2001): 198701. r)nxshortest_path_lengthr)Guveffs Y/var/www/html/env/lib/python3.13/site-packages/networkx/algorithms/efficiency_measures.pyrr sAX"))!22 J  Js  ..c[U5nXS- -nUS:waR[R"U5nSnUH.upVUR5HupxUS:dM USU- - nM M0 XB-nU$SnU$)aReturns the average global efficiency of the graph. The *efficiency* of a pair of nodes in a graph is the multiplicative inverse of the shortest path distance between the nodes. The *average global efficiency* of a graph is the average efficiency of all pairs of nodes [1]_. Parameters ---------- G : :class:`networkx.Graph` An undirected graph for which to compute the average global efficiency. Returns ------- float The average global efficiency of the graph. Examples -------- >>> G = nx.Graph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)]) >>> round(nx.global_efficiency(G), 12) 0.916666666667 Notes ----- Edge weights are ignored when computing the shortest path distances. See also -------- local_efficiency References ---------- .. [1] Latora, Vito, and Massimo Marchiori. "Efficient behavior of small-world networks." *Physical Review Letters* 87.19 (2001): 198701. r r)lenr all_pairs_shortest_path_lengthitems) rndenomlengthsg_effsourcetargetstargetdistances rrr>sT AA QKE z33A6&OF$+MMO a<Q\)E%4 '  L LcJ^U4SjT5n[U5[T5- $)a0Returns the average local efficiency of the graph. The *efficiency* of a pair of nodes in a graph is the multiplicative inverse of the shortest path distance between the nodes. The *local efficiency* of a node in the graph is the average global efficiency of the subgraph induced by the neighbors of the node. The *average local efficiency* is the average of the local efficiencies of each node [1]_. Parameters ---------- G : :class:`networkx.Graph` An undirected graph for which to compute the average local efficiency. Returns ------- float The average local efficiency of the graph. Examples -------- >>> G = nx.Graph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)]) >>> nx.local_efficiency(G) 0.9166666666666667 Notes ----- Edge weights are ignored when computing the shortest path distances. See also -------- global_efficiency References ---------- .. [1] Latora, Vito, and Massimo Marchiori. "Efficient behavior of small-world networks." *Physical Review Letters* 87.19 (2001): 198701. c3^># UH"n[TRTU55v M$ g7f)N)rsubgraph).0rrs r #local_efficiency..s'FAq(AaD)9::As*-)sumr)refficiency_lists` rrr{s%VGAFO  #a& ((r) __doc__networkxr networkx.exceptionrutilsr__all__ _dispatchablerrrrrr/sJ-' AZ .!.bZ 8!8vZ *)!*)r